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Make a set of numbers that use all the digits from 1 to 9, once and
once only. Add them up. The result is divisible by 9. Add each of
the digits in the new number. What is their sum? Now try some other
possibilities for yourself!

What happens to the perimeter of triangle ABC as the two smaller
circles change size and roll around inside the bigger circle?

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Stage: 3 Challenge Level:

There are 30 students in a class and it is found that in any subset
of 4 students from the class each student has exchanged Christmas
cards with the other three. Show that some students have exchanged
cards with all the other students in the class. How many such
students are there?

The NRICH Project aims to enrich the mathematical experiences of all learners. To support this aim, members of the
NRICH team work in a wide range of capacities, including providing professional development for teachers wishing to
embed rich mathematical tasks into everyday classroom practice. More information on many of our other activities
can be found here.